Stochastic dynamics and mean field approach in a system of three interacting species

TL;DR

This paper investigates the stochastic dynamics of a three-species predator-prey system with noise sources, revealing noise-induced oscillations and analyzing spatial-temporal behavior using mean field and coupled map lattice models.

Contribution

It introduces a combined approach using mean field theory and coupled map lattices to analyze noise effects in a three-species Lotka-Volterra system.

Findings

Noise induces oscillations in species densities.

Prey species exhibit anticorrelated behavior under noise.

Mean field and coupled map models produce consistent results.

Abstract

The spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied. To describe the spatial distributions of the species we use a model based on Lotka-Volterra equations. A correlated dichotomous noise acts on \beta, the interaction parameter between the two preys, and a multiplicative white noise affects directly the dynamics of each one of the three species. We study the time behaviour of the three species in single site for different values of the multiplicative noise intensity, finding noise-induced oscillations of the three species densities with an anticorrelated behaviour of the two preys. Afterwards, by considering a spatially extended system formed by a two-dimensional lattice with N sites and applying a mean field approach, we get the corresponding moment equations in Gaussian approximation. Within this formalism we obtain the time behaviour of the first and second order moments for different values of multiplicative noise intensity, with \beta(t) subject to the same dichotomous noise source. Finally, we compare our results with those obtained by using a coupled map lattice model, consisting of a time discrete version of the Lotka-Volterra equations.